This invention relates to the field of estimating radio frequency (RF) wave field characteristics in three dimensions (3D). Using existing point-to-point ray tracing programs to model the propagation of RF energy over a wide area is computationally expensive and has inherent limitations. For example, in refractive waveguides, ray treatments can result in caustics, where infinite rays cross the same focus points, leading to the incorrect calculation that the field intensity is infinite at those points (i.e., singularities). Less extreme issues arise from the infinitesimal nature of the ray paths, even without the occurrence of caustics. It is difficult to estimate wave intensity, for instance, in areas where the incidence of rays is sparse, as neighboring rays may have originated from very different initial angles, and may have very different phase paths, as a result. Such cases can arise because of the non-linearity of propagation through the refractive medium, or they may arise because of how the model was implemented by the user. There exists a need for a better way of estimating 3D, RF wave field characteristics.